Embedding of the Lie superalgebra $D(2, 1 ; α)$ into the Lie superalgebra of pseudodifferential symbols on $S^{1|2}$

Details Embedding of the Lie superalgebra $D(2, 1 ; α)$ into the Lie superalgebra of pseudodifferential symbols on $S^{1|2}$ Embedding of the Lie superalgebra $D(2, 1 ; α)$ into the Lie superalgebra of pseudodifferential symbols on $S^{1|2}$

2007-09-01

arxiv.org/abs/0709.0083v1

Physics

Mathematical Physics

19 pages, LaTex, to be published in J.Math. Phys

Scientific paper

10.1063/1.2793570

We obtain an embedding of a one-parameter family of exceptional simple Lie superalgebras $D(2, 1 ; \alpha)$ into the Lie superalgebra of pseudodifferential symbols on the supercircle $S^{1|2}$. Correspondingly, there is an embedding of $D(2, 1 ; \alpha)$ into a nontrivial central extension of the derived contact superconformal algebra $K'(4)$ realized in terms of $4\times 4$ matrices over a Weyl algebra.

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